Binary XOR Calculator
Perform a bitwise XOR operation on two binary numbers instantly. BinaryCon returns 1 when corresponding bits are different and 0 when the two bits are the same.
What Is a Binary XOR Calculator?
A Binary XOR Calculator performs the exclusive OR operation on two binary numbers. It compares corresponding bits independently and outputs 1 when the bits differ.
If both bits are the same, whether both are 0 or both are 1, XOR returns 0. This makes XOR particularly useful for detecting differences between bit patterns.
XOR 1100
—-
0110
Different bits → 1
The combinations 0 XOR 1 and 1 XOR 0 both produce a result of 1.
Matching bits → 0
The combinations 0 XOR 0 and 1 XOR 1 both produce a result of 0.
Binary XOR Truth Table
| A | B | A XOR B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
How to Calculate Binary XOR
Use a value containing only 0s and 1s, such as 101101.
Place the second value so its bit positions correspond with the first value.
If the values have different lengths, add leading zeros to the shorter one.
Return 1 when the bits differ and 0 when the two bits are identical.
Read all result bits from left to right to obtain the final XOR value.
Worked Example: 101101 XOR 110011
| Position | A | B | XOR |
|---|---|---|---|
| 1 | 1 | 1 | 0 |
| 2 | 0 | 1 | 1 |
| 3 | 1 | 0 | 1 |
| 4 | 1 | 0 | 1 |
| 5 | 0 | 1 | 1 |
| 6 | 1 | 1 | 0 |
Example: 1010 XOR 1100
XOR 1100
—-
0110
The middle two positions differ, so they become 1. The first and last positions match, so they become 0.
Binary XOR with Different Bit Lengths
For unsigned binary numbers, the shorter value can be padded on the left with zeros before the XOR operation.
0010 Then: 1011 XOR 0010 = 1001
XOR with Zero
XOR with an all-zero value leaves the original bit pattern unchanged.
This follows directly from 0 XOR 0 = 0 and
1 XOR 0 = 1.
XOR a Value with Itself
Any binary value XOR itself produces zero because every corresponding pair of bits is identical.
This identity is frequently used in low-level algorithms and programming.
XOR with All Ones
At a fixed bit width, XORing a value with all ones flips every bit.
Each 0 becomes 1 and each 1 becomes 0 because every input bit is compared against 1.
Binary XOR and Decimal Values
1100₂ = 12₁₀ XOR: 1010 XOR 1100 = 0110 Convert result: 0110₂ = 6₁₀ Therefore: 10 XOR 12 = 6
Why XOR Is Useful for Detecting Differences
XOR can highlight exactly which bit positions differ between two values. Every differing position becomes 1, while every matching position becomes 0.
The 1 bits in the XOR result identify the positions where the two original values differ.
XOR and Bit Toggling
XOR masks are useful for toggling selected bits. A mask bit of 1 flips the corresponding bit, while a mask bit of 0 leaves it unchanged.
Important Properties of XOR
| Property | Formula | Meaning |
|---|---|---|
| Commutative | A XOR B = B XOR A |
Operand order does not matter. |
| Associative | (A XOR B) XOR C = A XOR (B XOR C) |
Grouping does not change the result. |
| Identity | A XOR 0 = A |
Zero leaves the original value unchanged. |
| Self-inverse | A XOR A = 0 |
A value XOR itself becomes zero. |
| Reversible | (A XOR B) XOR B = A |
Applying the same XOR mask twice restores the original value. |
Binary XOR vs OR vs AND
| A | B | AND | OR | XOR |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 1 |
| 1 | 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 0 |
XOR differs from OR specifically when both bits are 1. OR returns 1 in that case, while XOR returns 0.
XOR Is Exclusive OR
The word exclusive means the result is true when exactly one of the two one-bit inputs is 1.
OR
0 OR 1 = 1, 1 OR 0 = 1, and 1 OR 1 = 1.
XOR
0 XOR 1 = 1 and 1 XOR 0 = 1, but 1 XOR 1 = 0.
Where Is Binary XOR Used?
Bit Toggling
Masks can flip selected bits without changing the remaining positions.
Difference Detection
XOR highlights exactly which corresponding bits differ between two values.
Error Detection
Parity calculations and simple error-detection systems frequently use XOR.
Cryptography Concepts
XOR is a fundamental reversible operation used within many cryptographic constructions.
Digital Logic
XOR gates are used in adders, parity circuits, comparators, and other digital systems.
Programming
Developers use XOR for masks, flags, bit manipulation, checksums, and low-level algorithms.
XOR in Binary Addition
XOR plays an important role in binary addition. For two single bits without considering a carry-in, XOR produces the sum bit.
| A | B | Sum Bit (XOR) | Carry Bit (AND) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
This combination of XOR and AND forms the basic logic of a half-adder circuit.
Common Binary XOR Mistakes
Remember that 1 XOR 1 equals 0, while 1 OR 1 equals 1.
Binary values contain only digits 0 and 1.
Align values from the right and pad the shorter unsigned value with leading zeros.
Applying the same XOR mask again restores the original value:
(A XOR B) XOR B = A.
Related BinaryCon Tools
Binary XOR Calculator FAQs
What is binary XOR?
What is 0 XOR 0?
0 XOR 0 = 0.
What is 0 XOR 1?
0 XOR 1 = 1.
What is 1 XOR 0?
1 XOR 0 = 1.
What is 1 XOR 1?
1 XOR 1 = 0 because the two input bits are the same.
What is 1010 XOR 1100?
What is 101101 XOR 110011?
What happens when a value is XORed with zero?
What happens when a value is XORed with itself?
Can XOR flip bits?
Why is XOR useful for comparing binary values?
What is the difference between XOR and OR?
Is XOR reversible?
C = A XOR B, then C XOR B = A.
Can XOR use different-length binary values?
Is XOR commutative?
A XOR B = B XOR A.
How is XOR used in binary addition?
Can BinaryCon process long XOR values?
Calculate Binary XOR Instantly
Use BinaryCon’s free Binary XOR Calculator to compare bit patterns, detect differences, toggle bits, learn exclusive OR logic, and verify results instantly.